Chemical
Reaction
Engineering
Third Edition
Octave Levenspiel
Department of Chemical Engineering
Oregon State University
John Wiley & Sons
New York Chichester Weinheim Brisbane Singapore Toronto
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Library of Congress Cataloging-in-Publication Data:
Levenspiel, Octave.
Chemical reaction engineering 1 Octave Levenspiel. - 3rd ed.
p.
cm.
Includes index.
ISBN 0-471-25424-X(cloth : alk. paper)
1. Chemical reactors.
I. Title.
TP157.L4 1999
6601.281-dc21
97-46872
CIP
Printed in the United States of America
Preface
Chemical reaction engineering is that engineering activity concerned with the
exploitation of chemical reactions on a commercial scale. Its goal is the successful
design and operation of chemical reactors, and probably more than any other
activity it sets chemical engineering apart as a distinct branch of the engineering profession.
In a typical situation the engineer is faced with a host of questions: what
information is needed to attack a problem, how best to obtain it, and then how
to select a reasonable design from the many available alternatives? The purpose
of this book is to teach how to answer these questions reliably and wisely. To
do this I emphasize qualitative arguments, simple design methods, graphical
procedures, and frequent comparison of capabilities of the major reactor types.
This approach should help develop a strong intuitive sense for good design which
can then guide and reinforce the formal methods.
This is a teaching book; thus, simple ideas are treated first, and are then
extended to the more complex. Also, emphasis is placed throughout on the
development of a common design strategy for all systems, homogeneous and
heterogeneous.
This is an introductory book. The pace is leisurely, and where needed, time is
taken to consider why certain assumptions are made, to discuss why an alternative
approach is not used, and to indicate the limitations of the treatment when
applied to real situations. Although the mathematical level is not particularly
difficult (elementary calculus and the linear first-order differential equation is
all that is needed), this does not mean that the ideas and concepts being taught
are particularly simple. To develop new ways of thinking and new intuitions is
not easy.
Regarding this new edition: first of all I should say that in spirit it follows the
earlier ones, and I try to keep things simple. In fact, I have removed material
from here and there that I felt more properly belonged in advanced books.
But I have added a number of new topics-biochemical systems, reactors with
fluidized solids, gadliquid reactors, and more on nonideal flow. The reason for
this is my feeling that students should at least be introduced to these subjects so
that they will have an idea of how to approach problems in these important areas.
iii
i~
Preface
I feel that problem-solving-the process of applying concepts to new situations-is essential to learning. Consequently this edition includes over 80 illustrative examples and over 400 problems (75% new) to help the student learn and
understand the concepts being taught.
This new edition is divided into five parts. For the first undergraduate course,
I would suggest covering Part 1 (go through Chapters 1 and 2 quickly-don't
dawdle there), and if extra time is available, go on to whatever chapters in Parts
2 to 5 that are of interest. For me, these would be catalytic systems (just Chapter
18) and a bit on nonideal flow (Chapters 11 and 12).
For the graduate or second course the material in Parts 2 to 5 should be suitable.
Finally, I'd like to acknowledge Professors Keith Levien, Julio Ottino, and
Richard Turton, and Dr. Amos Avidan, who have made useful and helpful
comments. Also, my grateful thanks go to Pam Wegner and Peggy Blair, who
typed and retyped-probably what seemed like ad infiniturn-to get this manuscript ready for the publisher.
And to you, the reader, if you find errors-no, when you find errors-or
sections of this book that are unclear, please let me know.
Octave Levenspiel
Chemical Engineering Department
Oregon State University
Corvallis, OR, 97331
Fax: (541) 737-4600
Contents
Notation /xi
Chapter 1
Overview of Chemical Reaction Engineering I1
Part I
Homogeneous Reactions in Ideal
Reactors I11
Chapter 2
Kinetics of Homogeneous Reactions I13
2.1
2.2
2.3
2.4
Concentration-Dependent Term of a Rate Equation I14
Temperature-Dependent Term of a Rate Equation I27
Searching for a Mechanism 129
Predictability of Reaction Rate from Theory 132
Chapter 3
Interpretation of Batch Reactor Data I38
3.1
3.2
3.3
3.4
Constant-volume Batch Reactor
Varying-volume Batch Reactor
Temperature and Reaction Rate
The Search for a Rate Equation
139
167
172
I75
Chapter 4
Introduction to Reactor Design 183
vi
Contents
Chapter 5
Ideal Reactors for a Single Reaction 190
5.1 Ideal Batch Reactors I91
52. Steady-State Mixed Flow Reactors 194
5.3 Steady-State Plug Flow Reactors 1101
Chapter 6
Design for Single Reactions I120
6.1
6.2
6.3
6.4
Size Comparison of Single Reactors 1121
Multiple-Reactor Systems 1124
Recycle Reactor 1136
Autocatalytic Reactions 1140
Chapter 7
Design for Parallel Reactions 1152
Chapter 8
Potpourri of Multiple Reactions 1170
8.1
8.2
8.3
8.4
8.5
8.6
8.7
Irreversible First-Order Reactions in Series 1170
First-Order Followed by Zero-Order Reaction 1178
Zero-Order Followed by First-Order Reaction 1179
Successive Irreversible Reactions of Different Orders 1180
Reversible Reactions 1181
Irreversible Series-Parallel Reactions 1181
The Denbigh Reaction and its Special Cases 1194
Chapter 9
Temperature and Pressure Effects 1207
9.1 Single Reactions 1207
9.2 Multiple Reactions 1235
Chapter 10
Choosing the Right Kind of Reactor 1240
Part I1
Flow Patterns, Contacting, and Non-Ideal
Flow I255
Chapter 11
Basics of Non-Ideal Flow 1257
11.1 E, the Age Distribution of Fluid, the RTD 1260
11.2 Conversion in Non-Ideal Flow Reactors 1273
Contents
Yii
Chapter 12
Compartment Models 1283
Chapter 13
The Dispersion Model 1293
13.1 Axial Dispersion 1293
13.2 Correlations for Axial Dispersion 1309
13.3 Chemical Reaction and Dispersion 1312
Chapter 14
The Tanks-in-Series Model 1321
14.1 Pulse Response Experiments and the RTD 1321
14.2 Chemical Conversion 1328
Chapter 15
The Convection Model for Laminar Flow 1339
15.1 The Convection Model and its RTD 1339
15.2 Chemical Conversion in Laminar Flow Reactors 1345
Chapter 16
Earliness of Mixing, Segregation and RTD 1350
16.1 Self-mixing of a Single Fluid 1350
16.2 Mixing of Two Miscible Fluids 1361
Part 111
Reactions Catalyzed by Solids 1367
Chapter 17
Heterogeneous Reactions - Introduction 1369
Chapter 18
Solid Catalyzed Reactions 1376
18.1
18.2
18.3
18.4
18.5
The Rate Equation for Surface Kinetics 1379
Pore Diffusion Resistance Combined with Surface Kinetics 1381
Porous Catalyst Particles I385
Heat Effects During Reaction 1391
Performance Equations for Reactors Containing Porous Catalyst
Particles 1393
18.6 Experimental Methods for Finding Rates 1396
18.7 Product Distribution in Multiple Reactions 1402
viii
Contents
Chapter 19
The Packed Bed Catalytic Reactor 1427
Chapter 20
Reactors with Suspended Solid Catalyst,
Fluidized Reactors of Various Types 1447
20.1
20.2
20.3
20.4
20.5
Background Information About Suspended Solids Reactors 1447
The Bubbling Fluidized Bed-BFB
1451
The K-L Model for BFB 1445
The Circulating Fluidized Bed-CFB
1465
The Jet Impact Reactor 1470
Chapter 21
Deactivating Catalysts 1473
21.1 Mechanisms of Catalyst Deactivation 1474
21.2 The Rate and Performance Equations 1475
21.3 Design 1489
Chapter 22
GIL Reactions on Solid Catalyst: Trickle Beds, Slurry
Reactors, Three-Phase Fluidized Beds 1500
22.1
22.2
22.3
22.4
22.5
The General Rate Equation 1500
Performanc Equations for an Excess of B 1503
Performance Equations for an Excess of A 1509
Which Kind of Contactor to Use 1509
Applications 1510
Part IV
Non-Catalytic Systems I521
Chapter 23
Fluid-Fluid Reactions: Kinetics I523
23.1 The Rate Equation 1524
Chapter 24
Fluid-Fluid Reactors: Design 1.540
24.1 Straight Mass Transfer 1543
24.2 Mass Transfer Plus Not Very Slow Reaction 1546
Chapter 25
Fluid-Particle Reactions: Kinetics 1566
25.1 Selection of a Model 1568
25.2 Shrinking Core Model for Spherical Particles of Unchanging
Size 1570
Contents
25.3
25.4
25.5
Rate of Reaction for Shrinking Spherical Particles 1577
Extensions 1579
Determination of the Rate-Controlling Step 1582
Chapter 26
Fluid-Particle Reactors: Design 1589
Part V
Biochemical Reaction Systems I609
Chapter 27
Enzyme Fermentation 1611
27.1 Michaelis-Menten Kinetics (M-M kinetics) 1612
27.2 Inhibition by a Foreign Substance-Competitive and
Noncompetitive Inhibition 1616
Chapter 28
Microbial Fermentation-Introduction and Overall
Picture 1623
Chapter 29
Substrate-Limiting Microbial Fermentation 1630
29.1 Batch (or Plug Flow) Fermentors 1630
29.2 Mixed Flow Fermentors 1633
29.3 Optimum Operations of Fermentors 1636
Chapter 30
Product-Limiting Microbial Fermentation 1645
30.1 Batch or Plus Flow Fermentors for n = 1 I646
30.2 Mixed Flow Fermentors for n = 1 1647
Appendix 1655
Name Index 1662
Subject Index 1665
ix
Notation
Symbols and constants which are defined and used locally are not included here.
SI units are given to show the dimensions of the symbols.
a , b ,..., 7,s,...
A
A, B,
...
A, B, C, D,
C
CM
c~
CLA,C ~ A
d
d
ge
ei(x)
interfacial area per unit volume of tower (m2/m3),see
Chapter 23
activity of a catalyst, see Eq. 21.4
stoichiometric coefficients for reacting substances A,
B, ..., R, s, .,.
cross sectional area of a reactor (m2), see Chapter 20
reactants
Geldart classification of particles, see Chapter 20
concentration (mol/m3)
Monod constant (mol/m3),see Chapters 28-30; or Michaelis constant (mol/m3), see Chapter 27
heat capacity (J/mol.K)
mean specific heat of feed, and of completely converted
product stream, per mole of key entering reactant (J/
mol A + all else with it)
diameter (m)
order of deactivation, see Chapter 22
dimensionless particle diameter, see Eq. 20.1
axial dispersion coefficient for flowing fluid (m2/s), see
Chapter 13
molecular diffusion coefficient (m2/s)
effective diffusion coefficient in porous structures (m3/m
solids)
an exponential integral, see Table 16.1
xi
~ i iNotation
E, E*, E**
Eoo, Eoc? ECO, Ecc
Ei(x)
8
f
A
F
F
G*
h
h
H
H
k
k, kt, II', k , k""
enhancement factor for mass transfer with reaction, see
Eq. 23.6
concentration of enzyme (mol or gm/m3),see Chapter 27
dimensionless output to a pulse input, the exit age distribution function (s-l), see Chapter 11
RTD for convective flow, see Chapter 15
RTD for the dispersion model, see Chapter 13
an exponential integral, see Table 16.1
effectiveness factor (-), see Chapter 18
fraction of solids (m3 solid/m3vessel), see Chapter 20
volume fraction of phase i (-), see Chapter 22
feed rate (molls or kgls)
dimensionless output to a step input (-), see Fig. 11.12
free energy (Jlmol A)
heat transfer coefficient (W/m2.K),see Chapter 18
height of absorption column (m), see Chapter 24
height of fluidized reactor (m), see Chapter 20
phase distribution coefficient or Henry's law constant; for
gas phase systems H = plC (Pa.m3/mol),see Chapter 23
mean enthalpy of the flowing stream per mole of A flowing
(Jlmol A + all else with it), see Chapter 9
enthalpy of unreacted feed stream, and of completely converted product stream, per mole of A (Jlmol A + all
else), see Chapter 19
heat of reaction at temperature T for the stoichiometry
as written (J)
heat or enthalpy change of reaction, of formation, and of
combustion (J or Jlmol)
reaction rate constant (mol/m3)'-" s-l, see Eq. 2.2
reaction rate constants based on r, r', J', J", J"', see Eqs.
18.14 to 18.18
rate constant for the deactivation of catalyst, see Chapter 21
effective thermal conductivity (Wlrn-K), see Chapter 18
mass transfer coefficient of the gas film (mol/m2.Pa.s),see
Eq. 23.2
mass transfer coefficient of the liquid film (m3 liquid/m2
surface.^), see Eq. 23.3
equilibrium constant of a reaction for the stoichiometry
as written (-), see Chapter 9
Notation
Q
r, r', J', J", J"'
rc
R
R, S,
R
...
xiii
bubble-cloud interchange coefficient in fluidized beds
(s-l), see Eq. 20.13
cloud-emulsion interchange coefficient in fluidized beds
(s-I), see Eq. 20.14
characteristic size of a porous catalyst particle (m), see
Eq. 18.13
half thickness of a flat plate particle (m), see Table 25.1
mass flow rate (kgls), see Eq. 11.6
mass (kg), see Chapter 11
order of reaction, see Eq. 2.2
number of equal-size mixed flow reactors in series, see
Chapter 6
moles of component A
partial pressure of component A (Pa)
partial pressure of A in gas which would be in equilibrium
with CAin the liquid; hence p z = HACA(Pa)
heat duty (J/s = W)
rate of reaction, an intensive measure, see Eqs. 1.2 to 1.6
radius of unreacted core (m), see Chapter 25
radius of particle (m), see Chapter 25
products of reaction
ideal gas law constant,
= 8.314 J1mol.K
= 1.987 cal1mol.K
= 0.08206 lit.atm/mol.K
recycle ratio, see Eq. 6.15
space velocity (s-l); see Eqs. 5.7 and 5.8
surface (m2)
time (s)
= Vlv, reactor holding time or mean residence time of
fluid in a flow reactor (s), see Eq. 5.24
temperature (K or "C)
dimensionless velocity, see Eq. 20.2
carrier or inert component in a phase, see Chapter 24
volumetric flow rate (m3/s)
volume (m3)
mass of solids in the reactor (kg)
fraction of A converted, the conversion (-)
X ~ V Notation
xA
moles Almoles inert in the liquid (-), see Chapter 24
moles Aimoles inert in the gas (-), see Chapter 24
yA
Greek symbols
a
S
6
a(t - to)
&A
E
8
8 = tl?
K"'
TI, ?",P, T'"'
@
4
P
p(MIN)
=
@
m3 wake/m3 bubble, see Eq. 20.9
volume fraction of bubbles in a BFB
Dirac delta function, an ideal pulse occurring at time t =
0 (s-I), see Eq. 11.14
Dirac delta function occurring at time to (s-l)
expansion factor, fractional volume change on complete
conversion of A, see Eq. 3.64
void fraction in a gas-solid system, see Chapter 20
effectiveness factor, see Eq. 18.11
dimensionless time units (-), see Eq. 11.5
overall reaction rate constant in BFB (m3 solid/m3gases),
see Chapter 20
viscosity of fluid (kg1m.s)
mean of a tracer output curve, (s), see Chapter 15
total pressure (Pa)
density or molar density (kg/m3 or mol/m3)
variance of a tracer curve or distribution function (s2),see
Eq. 13.2
V/v = CAoV/FAo,
space-time (s), see Eqs. 5.6 and 5.8
time for complete conversion of a reactant particle to
product (s)
= CAoW/FAo,
weight-time, (kg.s/m3), see Eq. 15.23
various measures of reactor performance, see Eqs.
18.42, 18.43
overall fractional yield, see Eq. 7.8
sphericity, see Eq. 20.6
instantaneous fractional yield, see Eq. 7.7
instantaneous fractional yield of M with respect to N, or
moles M formedlmol N formed or reacted away, see
Chapter 7
Symbols and abbreviations
BFB
BR
CFB
FF
bubbling fluidized bed, see Chapter 20
batch reactor, see Chapters 3 and 5
circulating fluidized bed, see Chapter 20
fast fluidized bed, see Chapter 20
Notation XV
@ = (p(M1N)
laminar flow reactor, see Chapter 15
mixed flow reactor, see Chapter 5
Michaelis Menten, see Chapter 27
see Eqs. 28.1 to 28.4
mw
PC
PCM
PFR
RTD
SCM
TB
molecular weight (kglmol)
pneumatic conveying, see Chapter 20
progressive conversion model, see Chapter 25
plug flow reactor, see Chapter 5
residence time distribution, see Chapter 11
shrinking-core model, see Chapter 25
turbulent fluidized bed, see Chapter 20
LFR
MFR
M-M
Subscripts
b
b
batch
bubble phase of a fluidized bed
of combustion
cloud phase of a fluidized bed
at unreacted core
deactivation
deadwater, or stagnant fluid
emulsion phase of a fluidized bed
equilibrium conditions
leaving or final
of formation
of gas
entering
of liquid
mixed flow
at minimum fluidizing conditions
plug flow
reactor or of reaction
solid or catalyst or surface conditions
entering or reference
using dimensionless time units, see Chapter 11
C
Superscripts
a, b,
n
0
...
order of reaction, see Eq. 2.2
order of reaction
refers to the standard state
X V ~ Notation
Dimensionless
groups
D
uL
vessel dispersion number, see Chapter 13
intensity of dispersion number, see Chapter 13
Hatta modulus, see Eq. 23.8 andlor Figure 23.4
Thiele modulus, see Eq. 18.23 or 18.26
Wagner-Weisz-Wheeler modulus, see Eq. 18.24 or 18.34
dup
Re = P
P
Sc = -
~g
Reynolds number
Schmidt number
Chapter
1
Overview of Chemical Reaction
Engineering
Every industrial chemical process is designed to produce economically a desired
product from a variety of starting materials through a succession of treatment
steps. Figure 1.1shows a typical situation. The raw materials undergo a number
of physical treatment steps to put them in the form in which they can be reacted
chemically. Then they pass through the reactor. The products of the reaction
must then undergo further physical treatment-separations, purifications, etc.for the final desired product to be obtained.
Design of equipment for the physical treatment steps is studied in the unit
operations. In this book we are concerned with the chemical treatment step of
a process. Economically this may be an inconsequential unit, perhaps a simple
mixing tank. Frequently, however, the chemical treatment step is the heart of
the process, the thing that makes or breaks the process economically.
Design of the reactor is no routine matter, and many alternatives can be
proposed for a process. In searching for the optimum it is not just the cost of
the reactor that must be minimized. One design may have low reactor cost, but
the materials leaving the unit may be such that their treatment requires a much
higher cost than alternative designs. Hence, the economics of the overall process
must be considered.
Reactor design uses information, knowledge, and experience from a variety
of areas-thermodynamics, chemical kinetics, fluid mechanics, heat transfer,
mass transfer, and economics. Chemical reaction engineering is the synthesis of
all these factors with the aim of properly designing a chemical reactor.
To find what a reactor is able to do we need to know the kinetics, the contacting
pattern and the performance equation. We show this schematically in Fig. 1.2.
I
t
I
I
Recycle
Figure 1.1 Typical chemical process.
I
2
Chapter 1 Overview of Chemical Reaction Engineering
Peformance equation
relates input to output
contacting pattern or how
materials flow through and
contact each other in the reactor,
how early or late they mix, their
clumpiness or state of aggregation.
By their very nature some materials
are very clumpy-for instance, solids
and noncoalescing liquid droplets.
Kinetics or how fast things happen.
If very fast, then equilibrium tells
what will leave the reactor. If not
so fast, then the rate of chemical
reaction, and maybe heat and mass
transfer too, will determine what will
happen.
Figure 1.2 Information needed to predict what a reactor can do.
Much of this book deals with finding the expression to relate input to output
for various kinetics and various contacting patterns, or
output = f [input, kinetics, contacting]
(1)
This is called the performance equation. Why is this important? Because with
this expression we can compare different designs and conditions, find which is
best, and then scale up to larger units.
Classification of Reactions
There are many ways of classifying chemical reactions. In chemical reaction
engineering probably the most useful scheme is the breakdown according to
the number and types of phases involved, the big division being between the
homogeneous and heterogeneous systems. A reaction is homogeneous if it takes
place in one phase alone. A reaction is heterogeneous if it requires the presence
of at least two phases to proceed at the rate that it does. It is immaterial whether
the reaction takes place in one, two, or more phases; at an interface; or whether
the reactants and products are distributed among the phases or are all contained
within a single phase. All that counts is that at least two phases are necessary
for the reaction to proceed as it does.
Sometimes this classification is not clear-cut as with the large class of biological
reactions, the enzyme-substrate reactions. Here the enzyme acts as a catalyst in
the manufacture of proteins and other products. Since enzymes themselves are
highly complicated large-molecular-weight proteins of colloidal size, 10-100 nm,
enzyme-containing solutions represent a gray region between homogeneous and
heterogeneous systems. Other examples for which the distinction between homogeneous and heterogeneous systems is not sharp are the very rapid chemical
reactions, such as the burning gas flame. Here large nonhomogeneity in composition and temperature exist. Strictly speaking, then, we do not have a single phase,
for a phase implies uniform temperature, pressure, and composition throughout.
The answer to the question of how to classify these borderline cases is simple.
It depends on how we choose to treat them, and this in turn depends on which
Chapter 1 Overview of Chemical Reaction Engineering
3
Table 1.1 Classification of Chemical Reactions Useful in Reactor Design
Noncatalytic
Catalytic
Most gas-phase reactions ..........................
Most liquid-phase reactions
.....................
Reactions in colloidal systems
------------ Fast reactions such as
burning
of
a
flame
Enzyme
and microbial reactions
.....................
..........................
Burning of coal
Ammonia synthesis
Roasting of ores
Oxidation of ammonia to proAttack of solids by acids
duce nitric acid
Cracking of crude oil
Heterogeneous Gas-liquid absorption
with reaction
Oxidation of SO2to SO3
Reduction of iron ore to
iron and steel
Homogeneous
description we think is more useful. Thus, only in the context of a given situation
can we decide how best to treat these borderline cases.
Cutting across this classification is the catalytic reaction whose rate is altered
by materials that are neither reactants nor products. These foreign materials,
called catalysts, need not be present in large amounts. Catalysts act somehow as
go-betweens, either hindering or accelerating the reaction process while being
modified relatively slowly if at all.
Table 1.1shows the classification of chemical reactions according to our scheme
with a few examples of typical reactions for each type.
Variables Affecting the Rate of Reaction
Many variables may affect the rate of a chemical reaction. In homogeneous
systems the temperature, pressure, and composition are obvious variables. In
heterogeneous systems more than one phase is involved; hence, the problem
becomes more complex. Material may have to move from phase to phase during
reaction; hence, the rate of mass transfer can become important. For example,
in the burning of a coal briquette the diffusion of oxygen through the gas film
surrounding the particle, and through the ash layer at the surface of the particle,
can play an important role in limiting the rate of reaction. In addition, the rate
of heat transfer may also become a factor. Consider, for example, an exothermic
reaction taking place at the interior surfaces of a porous catalyst pellet. If the
heat released by reaction is not removed fast enough, a severe nonuniform
temperature distribution can occur within the pellet, which in turn will result in
differing point rates of reaction. These heat and mass transfer effects become
increasingly important the faster the rate of reaction, and in very fast reactions,
such as burning flames, they become rate controlling. Thus, heat and mass transfer
may play important roles in determining the rates of heterogeneous reactions.
Definition of Reaction Rate
We next ask how to define the rate of reaction in meaningful and useful ways.
To answer this, let us adopt a number of definitions of rate of reaction, all
4
Chapter I Overview of Chemical Reaction Engineering
interrelated and all intensive rather than extensive measures. But first we must
select one reaction component for consideration and define the rate in terms of
this component i. If the rate of change in number of moles of this component
due to reaction is dN,ldt, then the rate of reaction in its various forms is defined
as follows. Based on unit volume of reacting fluid,
y . = -1
V
moles i formed
dNi=
(volume of fluid) (time)
dt
Based on unit mass of solid in fluid-solid systems,
l , , , , , i """"
mass of solid) (time)
Based on unit interfacial surface in two-fluid systems or based on unit surface
of solid in gas-solid systems,
I dNi = moles i formed
y ; = --
Based on unit volume of solid in gas-solid systems
1 dN, =
y!'t = -V, dt
moles i formed
(volume of solid) (time)
Based on unit volume of reactor, if different from the rate based on unit volume
of fluid,
1 dNi =
,.!"' = -V, dt
moles i formed
(volume of reactor) (time)
In homogeneous systems the volume of fluid in the reactor is often identical to
the volume of reactor. In such a case V and Vr are identical and Eqs. 2 and 6
are used interchangeably. In heterogeneous systems all the above definitions of
reaction rate are encountered, the definition used in any particular situation
often being a matter of convenience.
From Eqs. 2 to 6 these intensive definitions of reaction rate are related by
volume
mass of
(of fluid) ri = solid
(
)
surface
" = (of solid) r'
=
volume
of solid
(
vol~me
of
"= reactor
) (
)
ry
Chapter 1 Overview of Chemical Reaction Engineering
5
Speed of Chemical Reactions
Some reactions occur very rapidly; others very, very slowly. For example, in the
production of polyethylene, one of our most important plastics, or in the production of gasoline from crude petroleum, we want the reaction step to be complete
in less than one second, while in waste water treatment, reaction may take days
and days to do the job.
Figure 1.3 indicates the relative rates at which reactions occur. To give you
an appreciation of the relative rates or relative values between what goes on in
sewage treatment plants and in rocket engines, this is equivalent to
1 sec to 3 yr
With such a large ratio, of course the design of reactors will be quite different
in these cases.
*
1
t
Cellular rxs.,
industrial water
treatment plants
Human
at rest
Jet engines
...
wor'king
hard
...
Gases in porous
catalyst particles
*
Coal furnaces
Rocket engines
Figure 1.3 Rate of reactions
-Ji
=
Bimolecular rxs. in which
every collision counts, at
about -1 atm and 400°C
moles of A disappearing
m3of thing. s
Overall Plan
Reactors come in all colors, shapes, and sizes and are used for all sorts of
reactions. As a brief sampling we have the giant cat crackers for oil refining; the
monster blast furnaces for iron making; the crafty activated sludge ponds for
sewage treatment; the amazing polymerization tanks for plastics, paints, and
fibers; the critically important pharmaceutical vats for producing aspirin, penicillin, and birth control drugs; the happy-go-lucky fermentation jugs for moonshine;
and, of course, the beastly cigarette.
Such reactions are so different in rates and types that it would be awkward
to try to treat them all in one way. So we treat them by type in this book because
each type requires developing the appropriate set of performance equations.
6
Chapter 1 Overview of Chemical Reaction Engineering
/ EX4MPLB
1.1
THE ROCKET ENGINE
A rocket engine, Fig. El.l, burns a stoichiometric mixture of fuel (liquid hydrogen) in oxidant (liquid oxygen). The combustion chamber is cylindrical, 75 cm
long and 60 cm in diameter, and the combustion process produces 108 kgls of
exhaust gases. If combustion is complete, find the rate of reaction of hydrogen
and of oxygen.
1
~
C o m ~ l e t ecombustion
Figure E l . l
We want to evaluate
-rH2-1d N ~ 2
and
V dt
-yo,
1 dN0,
V dt
= --
Let us evaluate terms. The reactor volume and the volume in which reaction
takes place are identical. Thus,
Next, let us look at the reaction occurring.
molecular weight:
2gm
16 gm 18 gm
Therefore,
H,O producedls = 108 kgls - = 6 kmolls
(IlKt)
So from Eq. (i)
H, used
=
6 kmolls
0, used = 3 kmolls
Chapter 1 Overview of Chemical Reaction Engineering
l
and the rate of reaction is
3
-
- -
1
.--6 kmol - 2.829 X lo4 mol used
0.2121 m3
s
(m3of rocket) . s
1
-To = - 0.2121 m3
2
-
I
/
I
7
kmol
mol
3 -= 1.415 X lo4
s
Note: Compare these rates with the values given in Figure 1.3.
EXAMPLE 1.2
THE LIVING PERSON
A human being (75 kg) consumes about 6000 kJ of food per day. Assume that
the food is all glucose and that the overall reaction is
'
C,H,,O,+60,-6C02+6H,0,
from air
'breathe,
-AHr=2816kJ
out
Find man's metabolic rate (the rate of living, loving, and laughing) in terms of
moles of oxygen used per m3 of person per second.
We want to find
Let us evaluate the two terms in this equation. First of all, from our life experience
we estimate the density of man to be
Therefore, for the person in question
Next, noting that each mole of glucose consumed uses 6 moles of oxygen and
releases 2816 kJ of energy, we see that we need
6000 kJIday
2816 kJ1mol glucose
)(
)
6 mol 0,
mol 0,
= 12.8 day
1mol glucose
8
I
Chapter 1 Overview of Chemical Reaction Engineering
Inserting into Eq. (i)
1
=0.075 m3
12.8 mol 0, used
1day
mol 0, used
= 0.002
day
24 X 3600 s
m3 . s
Note: Compare this value with those listed in Figure 1.3.
PROBLEMS
1.1. Municipal waste water treatment plant. Consider a municipal water treatment plant for a small community (Fig. P1.1). Waste water, 32 000 m3/day,
flows through the treatment plant with a mean residence time of 8 hr, air
is bubbled through the tanks, and microbes in the tank attack and break
down the organic material
(organic waste)
+ 0,
microbes
C 0 2 + H,O
A typical entering feed has a BOD (biological oxygen demand) of 200 mg
O,/liter, while the effluent has a negligible BOD. Find the rate of reaction,
or decrease in BOD in the treatment tanks.
Waste water,
32,000 m3/day
t
2 0 0 mg O2
neededlliter
--I
Waste water
treatment plant
Clean water,
32,000 rn3/day
t
t
Mean residence
time t =8 hr
Zero O2 needed
Figure P1.l
1.2. Coal burning electrical power station. Large central power stations (about
1000 MW electrical) using fluidized bed combustors may be built some day
(see Fig. P1.2). These giants would be fed 240 tons of coallhr (90% C, 10%
Fluidized bed
\
50% of the feed
burns in these 1 0 units
Figure P1.2
Chapter 1 Overview of Chemical Reaction Engineering
9
H,), 50% of which would burn within the battery of primary fluidized beds,
the other 50% elsewhere in the system. One suggested design would use a
battery of 10 fluidized beds, each 20 m long, 4 m wide, and containing solids
to a depth of 1 m. Find the rate of reaction within the beds, based on the
oxygen used.
1.3. Fluid cracking crackers (FCC). FCC reactors are among the largest processing units used in the petroleum industry. Figure P1.3 shows an example
of such units. A typical unit is 4-10 m ID and 10-20 m high and contains
about 50 tons of p = 800 kg/m3porous catalyst. It is fed about 38 000 barrels
of crude oil per day (6000 m3/day at a density p = 900 kg/m3), and it cracks
these long chain hydrocarbons into shorter molecules.
To get an idea of the rate of reaction in these giant units, let us simplify
and suppose that the feed consists of just C,, hydrocarbon, or
If 60% of the vaporized feed is cracked in the unit, what is the rate of
reaction, expressed as - r r (mols reactedlkg cat. s) and as r"' (mols reacted1
m3 cat. s)?
Figure P1.3 The Exxon Model IV FCC unit.
Homogeneous Reactions
in Ideal Reactors
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Kinetics of Homogeneous Reactions 113
Interpretation of Batch Reactor Data I38
Introduction to Reactor Design I83
Ideal Reactors for a Single Reaction I90
Design for Single Reactions 1120
Design for Parallel Reactions 1152
Potpourri of Multiple Reactions 1170
Temperature and Pressure Effects 1207
Choosing the Right Kind of Reactor 1240
Chapter
2
Kinetics of Homogeneous
Reactions
Simple Reactor Types
Ideal reactors have three ideal flow or contacting patterns. We show these in
Fig. 2.1, and we very often try to make real reactors approach these ideals as
closely as possible.
We particularly like these three flow or reacting patterns because they are
easy to treat (it is simple to find their performance equations) and because one
of them often is the best pattern possible (it will give the most of whatever it is
we want). Later we will consider recycle reactors, staged reactors, and other flow
pattern combinations, as well as deviations of real reactors from these ideals.
The Rate Equation
Suppose a single-phase reaction aA + bB + rR
of reaction rate for reactant A is then
+ sS. The most useful measure
rate of disappearance of A
F(
"
\ h
1 dNA
= -\p
( note that this is an
-the
intensive measure
- (amount of
-
A disappearing)
(volume) (time)
(1)
minus sign
means disappearance
In addition, the rates of reaction of all materials are related by
Experience shows that the rate of reaction is influenced by the composition and
the energy of the material. By energy we mean the temperature (random kinetic
energy of the molecules), the light intensity within the system (this may affect
13